Question

use the right triangle abc to find the length of the line segment between point a and point b. now, find the exact length of the hypotenuse, c. that’s the length of the line segment between point a and point b. use square root notation to write the exact value of c. you can solve below or solve on paper and then enter your answer on zearn. the coordinate grid shows point b(-1,5), point c(7,5), point a(7,-3). the equation a² + b² = c² is given, with 8² + 8² = c². then find c.

Explanation:

Step1: Calculate \(8^2 + 8^2\)

First, find the value of \(8^2\), which is \(64\). So \(8^2 + 8^2 = 64 + 64\).
\(64 + 64 = 128\), so \(c^2 = 128\).

Step2: Solve for \(c\)

To find \(c\), take the square root of both sides. \(c=\sqrt{128}\). Simplify \(\sqrt{128}\) by factoring out the perfect square: \(128 = 64\times2\), so \(\sqrt{128}=\sqrt{64\times2}=\sqrt{64}\times\sqrt{2}=8\sqrt{2}\).

Answer:

\(8\sqrt{2}\)